Edge structure preserving image denoising

Image denoising is important in image analysis. It is often used for pre-processing images so that subsequent image analysis is more reliable. Besides noise removal, one important requirement for image denoising procedures is that they should preserve true image structures, such as edges. This paper proposes a novel denoising procedure which can preserve edges and major edge features (e.g., angles of the edges). Our method is based on nonparametric estimation of a discontinuous surface from noisy data, in the framework of jump regression analysis, because a monochrome image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects. Numerical studies show that this method works well in applications, compared to some existing image denoising procedures.